Adaptive Extended Kalman Filter for Orbit Estimation of GEO Satellites

Abstract

The aim of this paper is to develop Adaptive Extended Kalman Filter (AEKF) algorithm for the precise orbit estimation of GEO satellites (viz., GSAT-10 – Geostationary satellite and IRNSS-1A – Geosynchronous satellite) using two-way CDMA range measurements data from different ranging stations located in India. It brings forward the effectiveness of AEKF algorithm over Extended Kalman Filter (EKF) algorithm. EKF algorithm is adapted by updating process noise covariance (Q), measure of uncertainty in state dynamics during the time interval between measurement updates and measurement noise covariance (R), function of measurement update based on measurement residual. This paper addresses the modeling of all errors in measurement domain and the computation of measurement residual using observed and modeled measurement ranges for all stations. The filter incorporates non-linear model for measurement update, non-linear dynamic model for time update and estimation is carried out at every second. This paper also elaborates the development of indigenous full force propagation model considering all the perturbations during orbit prediction period for GEO Satellites. Adaptation of EKF algorithm in precise orbit estimation is done primarily for making the algorithm more robust by countering the uncertainties in process and measurement noises, resolving the problem of manual tuning of the filter and also by keeping the error covariance (P) consistent with real performance. Adaptation of Q is implemented based on the error in system states with respect to estimated states while Adaptation of R is implemented based on the error in observed measurements with respect to measurements obtained from estimated state vectors (aposteriori measurement expectation). Analysis of the estimated results using the above proposed method is carried out by comparison of Station-wise range residues for both the methods (AEKF and EKF). Consistency of obtained orbit for GEO Satellites are validated using overlapping technique for both AEKF and EKF methods, orbit estimated from these methods are also validated by comparing with batch least squares method and filter behavior is continuously monitored during data gaps by observing error covariance(P) for both the methods.

Keywords: Kalman Filtering, Process Noise Covariance, Measurement Noise Covariance, Orbit Estimation, CDMA